# When you multiply two numbers with exponents, should you add, subtract, multiply or divide the exponents?

Apr 8, 2016

Please see below

#### Explanation:

When we multiply two numbers with exponents, we add exponents only when they have common base.

As an example, when we multiply say $48 = 2 \times 2 \times 2 \times 2 \times 3 = {2}^{3} \times {3}^{1}$ with $36 = 2 \times 2 \times 3 \times 3 = {2}^{2} \times {3}^{2}$, then

$48 \times 36 = \left({2}^{3} \times {3}^{1}\right) \times \left({2}^{2} \times {3}^{2}\right) = {2}^{3 + 2} \times {3}^{1 + 2} = {2}^{5} \times {3}^{3}$

Similarly, when we divide two numbers with exponents, we should subtract the exponent of denominator from that of numerator provided they have common base.